Volume 69, Issue 12, 15 December 1978
Index of content:

The pair and direct correlation functions of an inhomogeneous fluid
View Description Hide DescriptionFunctional expansions are given relating the pair and direct correlation functions of an inhomogeneous fluid to the many body direct correlation functions of a homogeneous fluid. The exact expression for the pair correlation function to second order in density gradients contains a coupling between particle correlation and density inhomogeneity. In contrast to several local density correlation models, typical of those used recently in the theory of fluid interfaces, the exact theory predicts such coupling even for particles lying in the plane perpendicular to the direction of the density gradient. This means that an interface can never be viewed strictly as a stack of thin homogeneous phases. In the low density limit, the three local density approximations considered agree with the exact theory to first order in density gradients but not to second order.

On the bifurcation analysis of the liquid–solid instability in hard‐sphere systems
View Description Hide DescriptionRecent bifurcationanalyses of the BBGKY hierarchy for hard‐sphere systems are shown to be equivalent to Kirkwood’s linear response analysis. They suffer, therefore, from the same inconsistency which has been pointed out by Kunkin and Frisch. The decoupling scheme used also leads to an inconsistency in the stability analysis of the dynamic BBGKY hierarchy.

The generator coordinate method for molecular wavefunctions: A moment method and a simple intrinsic function
View Description Hide DescriptionAn extension of the generator coordinate method to the description of the electronic structure of molecules is presented. An exact formal solution to the Hill–Wheeler equation is obtained for a certain class of intrinsic functions, namely, those whose Hamiltonian and overlap kernels are of degenerate form. Since the exact kernels are used in the Hill–Wheeler equation, the variational principle is retained. The formal solution is represented by the set of moments of the generator coordinate with respect to the weighting function. The features of the method are illustrated by application to the hydrogen molecule. A simple trial intrinsic function and a PPP Hamiltonian are used to describe the π‐electron structure of three linear conjugated polyenes (1,3‐butadiene; 1,3,5‐hexatriene; and 1,3,5,7‐octatetraene). A significant part of the apparent ground statecorrelation energy is recovered for each molecule and π‐electron excited state energies are also calculated. These results are compared with PPP CI calculations and the limitations of this simple trial intrinsic function are discussed.

On the contribution of the exciton–photon interaction to the exciton absorption line shape in the spatially inhomogeneous wave model: Application to the a‐singlet exciton of naphthalene
View Description Hide DescriptionThe problem of determining the contribution of the e x c i t o n–p h o t o n coupling to the absorption line shape or width of an exciton is addressed. In this regard, both the spatially homogeneous (polariton) and inhomogeneous wave models are considered. For the latter model, the theory is complex although a line shape expression is derived for the case of high exciton velocity and low oscillator strength. The related problem of determining the conditions under which the strong exciton–photon coupling limit is attained is also discussed. It is in this limit that light attenuation is independent of the oscillator strength. The theory plus new experimental data on the aexciton of n a p h t h a l e n e argue for the inadequacy of the polariton model. On the other hand, reasonable agreement between the data and the spatially inhomogeneous wave theory developed here is obtained. Thus, it is possible to estimate that the exciton–photon coupling contribution to the a‐exciton linewidth is 0.26 cm^{−1}. This is the major portion of the 2 K linewidth of 0.3 cm^{−1}.

Ultraviolet dispersion of the donor–acceptor charge transfer contribution to the second order hyperpolarizability
View Description Hide DescriptionWe have measured for the first time electric field induced optical mixing (ω+2ω=3ω) in the liquid state. Two molecules DANS (t r a n s‐4‐dimethylamino‐4′‐nitrostilbene) and p‐NA (p‐nitroaniline) possessing large i n t r amolecular charge transfer interactions were used and the second order mixing hyperpolariabilities β (3ω) were determined to be β (3ω) = (−7.2±2.6i) ×10^{−28} and β (3ω) = (+9.6±38i) ×10^{−30} esu for DANS and p‐NA, respectively, with 3ω=3.50 eV. Combining these measurements with the simple two level quantum mechanical model yields the theoretical prediction of β (2ω) = (+38+15i) ×10^{−28} and β (2ω) = (+48+5.3i) ×10^{−30} esu for the second harmonic hyperpolarizability of DANS and p‐NA, respectively. These predictions are not in good agreement with the experimental values ‖β (2ω) ‖ =2.1×10^{−28} esu (obtained using the measurements of Oudar and Chemla) and β (2ω) =+22×10^{−30} esu.

Reactive dynamics for diffusive barrier crossing
View Description Hide DescriptionA theory is presented for intramolecular reactions A?B regarded as potential barrier crossing between two stable states A and B in the large friction limit. This limit, in which dynamics are governed by spatial diffusion in the potential, is an important example of extreme deviation from transition state theory predictions. Our theory expresses the full reaction rate constants in terms of simpler contributions: (a) the barrier rate constants and (b) the internal rate constants. The former depend solely on dynamics near the barrier top and govern the rate when stable state internal equilibrium is maintained. The latter depend solely on internal equilibration dynamics in the stable states A and B (defined away from the barrier top). The internal rate constants correct the barrier rate constants for stable state internal nonequilibrium effects. These two contributions are discussed in dynamical terms in some detail. Our theoreticalrate constants are evaluated and compared with the rate constants observed by monitoring population decays obtained by direct numerical integration of the Smoluchowski equation. A simple minimum principle predicts the reaction rate constants with high accuracy at any value of the barrier height. For high barriers, our predictions approach (but are more accurate than) those of the classic approximate analysis of Kramers. For very low barriers (e.g., 1.6k_{B} T), internal nonequilibrium effects neglected by Kramers are found by our theory to account for approximately 33% of the rate constant.

Initial condition effects for diffusive barrier crossing
View Description Hide DescriptionA formulation and analysis of transient initial condition effects on reaction is given for the diffusive limit of barrier crossing between two stable chemical states. We focus on the case where the system is initially prepared in the high energy intermediate barrier region located between the stable states. It is shown how branching fluxes into and branching probabilities for stable states can be both calculated for and determined from analysis of stable state population dynamics.

Crossed molecular beam study of the reactions of methyl bromide with potassium and rubidium
View Description Hide DescriptionUsing the crossed molecular beam method, the yields of the alkali halide product MBr from the exoergic reactions CH_{3}Br+M→MBr+CH_{3} (M≡K, Rb) have been measured as a function of relative translational energy up to 0.9 and 1.3 eV for K and Rb, respectively. Supersonic seeded beams of CH_{3}Br are crossed with thermal alkali beams and the in‐plane angular distribution of MBr measured at different average relative translational energies ?_{tr}. The reactions are found to have appreciable energy thresholds, 0.24±0.06 and 0.20±0.06 eV for the K and Rb‐reactions, respectively. The product yields increase monotonically with ?_{tr} above threshold. The postthreshold energy dependence of the cross sections has been obtained by deconvoluting these data from the crossed beam velocity distributions. The MBr angular distributions are characteristic of a direct, rebound mechanism, with a large fraction of the available energy going into product translation. The average recoil energy ?′_{tr} of the product MBr increases linearly with ?_{tr} (d?′_{tr}/d?_{tr}?0.73). The present data for the M+CH_{3}Br systems are compared with previous results for the analogous CH_{3}I reactions and with predictions of several theoretical models. The significantly higher activation barriers for the CH_{3}Br reactions account for their smaller thermal reaction rate constants relative to the analogous CH_{3}I reactions (from early flame experiments).

Elastic scattering and rotational excitation in ion‐molecule collisions. II. Li^{+}–H_{2} and H^{+}–H_{2} collisions
View Description Hide DescriptionA general semiclassical treatment of elasticscattering and of rotational excitation in ion–molecule collisions is presented. When the orbits associated with the different channels corresponding to the internal modes do not differ significantly, simplification occurs and the internal degrees of freedom can then be coupled to the relative motion via the introduction of an optical potential (which in turn depends on the transition amplitudes). Total energy is consequently conserved. An expression is derived for the inelastic scattering amplitude which acknowledges various interference effects and possible rainbow scattering. With all phase‐information supressed, the procedure, when compared with the full quantum‐mechanical results, reproduces the background elastic and inelastic scattering in Li^{+}–H_{2} and in H^{+}–H_{2}collisions. Restoration of the phases, particularly of the eikonal or action phases associated with the different classical paths that contribute to a specified scattering angle, produces the interference oscillations present in the differential cross section for scattering angles less than the rainbow angle. The method, when compared with the full quantal procedure, is remarkably efficient and accurate.

Lattice dynamics of the ethylene crystal with interaction potentials from a b i n i t i o calculations
View Description Hide DescriptionThe long range (electrostatic, dispersion, induction) and short range (exchange and penetration) interaction energy between ethylene molecules has been calculated by a b i n i t i o methods as a function of the molecular orientations and distances. The results, when fitted with an exp‐6‐1 atom–atom potential and used in a harmonic lattice dynamics calculation on the ethylene crystal, yield fair agreement with the experimental structure data, ir and Raman phonon frequencies. Although the fit with the atom–atom potential is reasonably good, some specific deviations from the a b i n i t i o results indicate the importance of the effects of chemical bonding on the intermolecular potential (leading to noncentral and nonpairwise additive atom–atom forces). The usual empirical atom–atom potentials are grossly corroborated, their main defect being the neglect or underestimate of electrostatic (quadrupole–quadrupole) interactions.

A b i n i t i o configuration interaction study of the low‐lying electronic states of MgH
View Description Hide DescriptionA b i n i t i oconfiguration interaction calculations have been performed on the X ^{2}Σ^{+}, A ^{2}Π, and B′ ^{2}Σ^{+} states of MgH. Numerical values for the potential curves have been obtained for 23 internuclear distances between 2.2 and 9.5 a _{0}. Dipole and transition moment functions have also been calculated. Spectroscopic constants obtained from the calculated potential curves are found to be in good agreement with experimental data; the maximum errors in R _{ e }, D _{ e }, T _{ e }, and ω_{ e } are 0.003 nm, 0.09 eV, 0.05 eV, and 38 cm^{−1}, respectively. The calculated band absorption oscillator strength for the X–A transition of 0.161 is believed to have ±20% accuracy.

Nuclear corrections to molecular properties. VI. Vibrational transition moments in asymmetric‐top molecules
View Description Hide DescriptionA general expansion is derived for the transition moment between two nondegenerate vibrational states of a polyatomic molecule. This analysis is combined with a b i n i t i osurfaces for the potential energy and the dipole moment of water vapor to predict integrated band absorption intensities. Calculations are compared with experiment for several transitions which originate in the zero‐point vibrational state.

Deuterium NMR study of molecular order and reorientation in the nematic phase of p‐methoxy‐d _{3}‐benzylidene‐d _{1}‐p‐n‐butyl‐d _{9}‐aniline
View Description Hide DescriptionThe deuterium quadrupole doublet splittings and spin–lattice relaxation times (T _{1}) are measured as a function of temperature in the nematic phase of p‐methoxy‐d _{3}‐benzylidene‐d _{1}‐p‐n‐butyl‐d _{9}‐aniline (MBBA‐d _{13}). It is shown that a single order parameter tensor is sufficient to fully describe the orientational order of the molecule even though the molecule is nonrigid. The molecular conformational averages, which are different for various C–D bonds, result in resolved deuterium NMRspectra from which the T _{1} for each deuteron site can be measured. While the simplest approach in treating order director fluctuations, in which molecular reorientations and collective fluctuation modes are assumed to be uncoupled, fails to explain our T _{1} data for all deuterons, Freed’s treatment of spin relaxation in liquid crystals does give a qualitative explanation. Using this theory, molecular reorientation times for different deuteron sites are estimated.

Laser‐excited resonant isotopic V→V energy transfer: H^{35}Cl–H^{37}Cl, H^{79}Br–H^{81}Br, D^{35}Cl–D^{37}Cl, and D^{79}Br–D^{81}Br
View Description Hide DescriptionAn isotopically selective transverse discharge chemical laser coupled with infrared fluorescence techniques is used to measure vibration‐to‐vibration energy transfer rates between v=1 levels of the isotopic species H ^{35}Cl?H^{37}Cl, H ^{79}Br?H ^{81}Br, D ^{35}Cl?D ^{37}Cl, and D ^{79}Br?D ^{81}Br. The measured rate constants are k _{HCl}= (1.91±0.04) ×10^{−11}, k _{HBr}= (1.50±0.06) ×10^{−11}, k _{DCl}= (1.18±0.08) ×10^{−11}, and k _{DBr}= (8.34±0.17) ×10^{−12} cm^{3} molecule^{−1} sec^{−1}. All of the processes are nearly resonant and the rates for the hydrogenated species are on the order of one‐tenth gas‐kinetic. The rates for DCl and DBr are found to be 1.6 and 1.8 times slower than the corresponding hydrogen halides. Direct comparison of the results with theoretical predictions for such resonantenergy transfer processes shows disagreement, indicating that further development of theoretical methods for these systems is desirable.

Absolute elastic differential electron scattering cross sections in the intermediate energy region. IV. CO
View Description Hide DescriptionUsing a crossed electron beam–molecular beam scattering geometry and a relative‐flow technique, ratios of elastic differential cross sections of CO to those of He have been measured at electron impact energies of 3, 5, 7.5, 9.9, 15, 20, 30, 50, 75, and 100 eV. At each energy, an angular range of 15° to 130° has been covered. These ratios have been multiplied by previously known He elastic differential cross sections to obtain elastic differential cross sections for CO. Since pure rotational excitations were not resolved, the elastic differential cross sections are a sum of elastic and pure rotational excitations at room temperature. From a knowledge of differential cross sections (DCS), integral and momentum transfer cross sections have been calculated. Both the DCS and integral cross sections are compared at 50, 75, and 100 eV to a recent two‐potential theory of e–molecule scattering. Present results show that the isoelectronic molecules CO and N_{2} have very similar magnitudes and shapes of their differential cross sections.

Vibrational relaxation in HCl–CO_{2} and HCl–N_{2}O mixtures studied by the laser‐induced fluorescence method
View Description Hide DescriptionRate constants k _{M–HCl} and k _{HCl–M} for the energy transfer between the vibrational levels 00^{0}1 of M=CO_{2} or N_{2}O and v=1 of HCl have been measured from 300 to about 900 K using the laser induced‐fluorescence method. The V–R T de‐excitation rates k ^{HCl} _{M} of M(00^{0}1) by HCl, and k ^{M} _{HC1} of HCl(v=1) by M have also been determined from measurements of the relaxation constants versus the molar fraction of M in the mixture. These rates are found to be on the same order of magnitude as the V–V transfer rates k _{M–HCl} and k _{HCl–M}, respectively. The V–V transfer and V–R T de‐excitation rates are evaluated from a method, developed by Shin, on the basis of a transfer of vibrational energy into rotational energy of HCl, and the calculated values are compared to the experimental results.

A model for the surface of molten salt. II. Electroneutrality and parameter changes
View Description Hide DescriptionThe Fowler model for an interface, which assumes two‐particle distribution functions to be those of bulk liquid whenever both particles are on the liquid side of a geometric dividing surface and zero otherwise, gives ridiculous results for a molten salt. A correction to ensure local electroneutrality, demanded by the Coulombic forces, re‐establishes qualitative agreement with reality. Equations for the electroneutrality correction (previously made only approximately) are given and solved by a variational technique. A simplified route to the bulk liquid distribution functions is developed; this permits experimentation with changes in parameters in the reduced primitive model used for the molten salt. The effect of such changes on calculated surface properties is investigated, and further improvements in the model discussed.

Interspecies vibrational energy flow in CO_{2} or N_{2}O mixtures with the series of deuterated methanes
View Description Hide DescriptionTime‐resolved laser‐induced infrared fluorescence was used to study the rates of deactivation of vibrationally excited CO_{2} and N_{2}O by the series of deuterated methanes CH_{ n }D_{4−n }, where n=0–4. Rates varied from 4.7 msec^{−1} torr^{−1} for CO_{2}–CH_{4} to 199 msec^{−1} torr^{−1} for N_{2}O–CD_{4}. Within experimental error, the deactivation probabilities for CO_{2} or N_{2}O by the same collision partner are identical. The rates observed were determined to increase linearly with the number of deuterons per substituted methane, and thus with the number of C–D stretches nearly resonant with the 001 state of CO_{2} or N_{2}O. The results are interpreted by examining the role that rotational state changes of the collision partners can play in reducing the vibrational energy defect, thus minimizing the amount of energy that must go into translations.

Steady states in hot atom chemistry
View Description Hide DescriptionA detailed comparison is made with the predictions of the hydrodynamic steady state theory of hot atom reactions developed by Keizer [J. Chem. Phys. 58, 4524 (1973)] and those obtained from a more precise moment method solution of the Boltzmann equation. Agreement is found to occur only if there is a good separation in the time scale for reactive collisions and the time scale for energy redistribution in elastic collisions. This requires that the system parameters, which includes mass ratios and cross sections, be such that the reaction proceeds slowly relative to the rate of elastic collisions. The steady state theory was intended to be a qualitative theory of hot atom reactions and fulfills that expectation for systems that possess the neccesary separation in relaxation times.

Resonance Raman spectra of copper tetraphenylporphyrin: Effects of strong vibronic coupling on excitation profiles and the absorption spectrum
View Description Hide DescriptionRaman excitation profiles of copper tetraphenylporphyrin have been obtained and interpreted in terms of strong vibronic coupling. The Duschinsky mixing of normal modes in the excited Q electronic state has a dominant effect on the excitation profiles and the absorptionspectrum. A general theoretical technique for calculating the vibronic states of molecules is described and applied to metalloporphyrins. The analytical expressions obtained from a new perturbation treatment of the vibronic problem permit a detailed physical understanding of strong coupling influences and interference effects observed in copper tetraphenylporphyrin excitation spectra. A modified interpretation of the Q band absorption is indicated.